We present proper motions for the Large & Small Magellanic Clouds (LMC & SMC) based on three epochs of textit{Hubble Space Telescope} data, spanning a $sim 7$ yr baseline, and centered on fields with background QSOs. The first two epochs, the subject
of past analyses, were obtained with ACS/HRC, and have been reanalyzed here. The new third epoch with WFC3/UVIS increases the time baseline and provides better control of systematics. The three-epoch data yield proper motion random errors of only 1-2% per field. For the LMC this is sufficient to constrain the internal proper motion dynamics, as will be discussed in a separate paper. Here we focus on the implied center-of-mass proper motions: mu_W(LMC) = -1.910 +/- 0.020 mas/yr, mu_N(LMC) = 0.229 +/- 0.047 mas/yr, and mu_W(SMC) = -0.772 +/- 0.063 mas/yr, mu_N(SMC) = -1.117 +/- 0.061 mas/yr. We combine the results with a revised understanding of the solar motion in the Milky Way to derive Galactocentric velocities: v_{tot,LMC} = 321 +/- 24 km/s and v_{tot,SMC} = 217 +/- 26 km/s. Our proper motion uncertainties are now dominated by limitations in our understanding of the internal kinematics and geometry of the Clouds, and our velocity uncertainties are dominated by distance errors. Orbit calculations for the Clouds around the Milky Way allow a range of orbital periods, depending on the uncertain masses of the Milky Way and LMC. Periods $lesssim 4$ Gyr are ruled out, which poses a challenge for traditional Magellanic Stream models. First-infall orbits are preferred (as supported by other arguments as well) if one imposes the requirement that the LMC and SMC must have been a bound pair for at least several Gyr.
We study the dynamics of the Magellanic Clouds in a model for the Local Group whose mass is constrained using the timing argument/two-body limit of the action principle. The goal is to evaluate the role of M31 in generating the high angular momentum
orbit of the Clouds, a puzzle that has only been exacerbated by the latest $HST$ proper motion measurements. We study the effects of varying the total Local Group mass, the relative mass of the Milky Way and M31, the proper motion of M31, and the proper motion of the LMC on this problem. Over a large part of this parameter-space we find that tides from M31 are insignificant. For a range of LMC proper motions approximately $3sigma$ higher than the mean and total Local Group mass $> 3.5times 10^{12} M_odot$, M31 can provide a significant torque to the LMC orbit. However, if the LMC is bound to the MW, then M31 is found to have negligible effect on its motion and the origin of the high angular momentum of the system remains a puzzle. Finally, we use the timing argument to calculate the total mass of the MW-LMC system based on the assumption that they are encountering each other for the first time, their previous perigalacticon being a Hubble time ago, obtaining $M_{rm MW} + M_{rm LMC} = (8.7 pm 0.8) times 10^{11} M_odot$.
We review our understanding of the kinematics of the LMC and the SMC, and their orbit around the Milky Way. The line-of-sight velocity fields of both the LMC and SMC have been mapped with high accuracy using thousands of discrete traces, as well as H
I gas. The LMC is a rotating disk for which the viewing angles have been well-established using various methods. The disk is elliptical in its disk plane. The disk thickness varies depending on the tracer population, with V/sigma ranging from 2-10 from the oldest to the youngest population. For the SMC, the old stellar population resides in a spheroidal distribution with considerable line-of-sight depth and low V/sigma. Young stars and HI gas reside in a more irregular rotating disk. Mass estimates based on the kinematics indicate that each Cloud is embedded in a dark halo. Proper motion measurements with HST show that both galaxies move significantly more rapidly around the Milky Way than previously believed. This indicates that for a canonical 10^12 solar mass Milky Way the Clouds are only passing by us for the first time. Although a higher Milky Way mass yields a bound orbit, this orbit is still very different from what has been previously assumed in models of the Magellanic Stream. Hence, much of our understanding of the history of the Magellanic System and the formation of the Magellanic Stream may need to be revised. The accuracy of the proper motion data is insufficient to say whether or not the LMC and SMC are bound to each other, but bound orbits do exist within the proper motion error ellipse.
In HST Cycles 11 and 13 we obtained two epochs of ACS/HRC data for fields in the Magellanic Clouds centered on background quasars. We used these data to determine the proper motions of the LMC and SMC to better than 5% and 15% respectively. The resul
ts had a number of unexpected implications for the Milky Way-LMC-SMC system. The implied three-dimensional velocities were larger than previously believed and close to the escape velocity in a standard 10^12 solar mass Milky Way dark halo, implying that the Clouds may be on their first passage. Also, the relative velocity between the LMC and SMC was larger than expected, leaving open the possibility that the Clouds may not be bound to each other. To further verify and refine our results we requested an additional epoch of data in Cycle 16 which is being executed with WFPC2/PC due to the failure of ACS. We present the results of an ongoing analysis of these WFPC2 data which indicate good consistency with the two-epoch results.
